Motion through a turbulently moving Inviscid Liquid, 351 



average velocity of the turbulent motion of the fluid. This 

 might seem to go far towards giving probability to the vortex 

 theory of the luminiferous ether, were it not for the doubtful 

 proviso at the end of § 20. 



22. If the undisturbed condition of the medium be a stable 

 symmetrical distribution of vortex-rings the suggested vitia- 

 tion by "rearrangement" cannot occur. For example, let it 

 be such as is represented in fig. 1, where the small white and 



Fig. 1. 



I 



n 



p 



u 



P 



4 



\ 



J 



o 







rN 



n 



Q 



black circles represent cross sections of the rings : the white 

 where the rotation is opposite to, and the black where it is in 

 the same direction as, the rotation of the hands of a watch 

 placed on the diagram facing towards the spectator. Imagine 

 first each vortex-ring to be in a portion of the fluid contained 

 within a rigid rectangular box, of which four sides are indi- 

 cated by the fine lines crossing one another at right angles 

 throughout the diagram ; and the other pair are parallel to 

 the paper, at any distance asunder we like to imagine. Sup- 

 posing the volume of rotationally moving portion of the fluid 

 constituting the ring to be given, there is clearly one deter- 

 minate shape, and diametral magnitude, in which it must be 

 given in order that the motion may be steady. Let it be so 

 given, and fill space with such rectangular boxes of vortices 

 arranged facing one another oppositely in the manner shown 



